quri_parts.chem.mol package#

class ActiveSpace(n_active_ele, n_active_orb, active_orbs_indices=None)#

Bases: object

An immutable (frozen) dataclass representing a active space.

Parameters:

  • n_active_ele (int) –

  • n_active_orb (int) –

  • active_orbs_indices (Sequence[int] | None) –

n_active_ele: int#

number of active electrons.

n_active_orb: int#

number of active orbitals.

active_orbs_indices: Sequence[int] | None = None#

sequence of spatial orbital indices of the active orbitals.

cas(n_active_ele, n_active_orb, active_orbs_indices=None)#

Convenient function for constructing the active space.

Parameters:

  • n_active_ele (int) –

  • n_active_orb (int) –

  • active_orbs_indices (Sequence[int] | None) –

Return type:

ActiveSpace

class ActiveSpaceMolecularOrbitals(mo, active_space)#

Bases: ActiveSpaceMolecularOrbitalsBase

Represents a data of the active space for the molecule.

Parameters:
property n_electron: int#

Returns a number of electrons.

property spin: int#

Returns the total spin of the electrons.

property n_active_ele: int#

Returns the number of active electrons.

property n_core_ele: int#

Returns the number of core electrons.

property n_ele_alpha: int#

Return the number of spin up electrons.

property n_ele_beta: int#

Return the number of spin down electrons.

property n_spatial_orb: int#

Returns the number of spatial orbitals.

property n_active_orb: int#

Returns the number of active orbitals.

property n_core_orb: int#

Returns the number of core orbitals.

property n_vir_orb: int#

Returns the number of virtual orbitals.

property mo_coeff: ndarray[Any, dtype[complex128]]#

Returns molecular orbital coefficients.

get_core_and_active_orb()#

Returns a set of core and active orbitals.

The output orbitals are represented as the spatial orbital.

Return type:

tuple[Sequence[int], Sequence[int]]

orb_type(mo_index)#

Returns a type of the given orbital index.

Parameters:

mo_index (int) – Orbital index.

Return type:

OrbitalType

class ActiveSpaceMolecularOrbitalsBase(*args, **kwargs)#

Bases: MolecularOrbitals, ABC

abstract property n_active_ele: int#
abstract property n_core_ele: int#
abstract property n_active_orb: int#

Returns the number of active orbitals.

abstract property n_core_orb: int#

Returns the number of core orbitals.

abstract property n_vir_orb: int#

Returns the number of virtual orbitals.

abstract get_core_and_active_orb()#
Return type:

tuple[Sequence[int], Sequence[int]]

abstract orb_type(mo_index)#
Parameters:

mo_index (int) –

Return type:

OrbitalType

class AO1eInt(*args, **kwargs)#

Bases: Protocol

Interface protocol for an atomic orbital one-electron integral.

abstract property array: ndarray[Any, dtype[complex128]]#

Returns integral as numpy ndarray.

abstract to_mo1int(mo_coeff)#

This method converts an atomic orbital one-electron integral into the molecular orbital one-electron integral.

Parameters:

mo_coeff (ndarray[Any, dtype[complex128]]) – molecular orbital coefficients.

Return type:

SpinMO1eInt

class AO2eInt(*args, **kwargs)#

Bases: Protocol

Interface protocol for an atomic orbital two-electron integral.

abstract property array: ndarray[Any, dtype[complex128]]#

Returns integral as numpy ndarray.

abstract to_mo2int(mo_coeff)#

This method converts an atomic orbital two-electron integral into the molecular orbital two-electron integral.

Parameters:

mo_coeff (ndarray[Any, dtype[complex128]]) – molecular orbital coefficients.

Return type:

SpinMO2eInt

class AOeIntSet(*args, **kwargs)#

Bases: Protocol

AOeIntSet holds a constant and the atomic orbital electron integrals.

constant: float#

constant.

ao_1e_int: AO1eInt#

atomic orbital one-electron integral AO1eInt.

ao_2e_int: AO2eInt#

atomic orbital two-electron integral AO2eInt.

to_full_space_mo_int(mo)#

Compute the full space spin mo integral.

Parameters:

mo (MolecularOrbitals) –

Return type:

SpinMOeIntSet

to_active_space_mo_int(active_space_mo)#

Compute the active space spin mo integral.

Parameters:

active_space_mo (ActiveSpaceMolecularOrbitalsBase) –

Return type:

SpinMOeIntSet

class AO1eIntArray(ao1eint_array)#

Bases: AO1eInt

Parameters:

ao1eint_array (npt.NDArray[np.complex128]) –

property array: ndarray[Any, dtype[complex128]]#

Returns the ao 1-electron integrals in physicist’s notation.

to_spatial_mo1int(mo_coeff)#

Returns the spatial mo 1-electron integrals in physicist’s notation.

Parameters:

mo_coeff (ndarray[Any, dtype[complex128]]) –

Return type:

SpatialMO1eIntArray

to_mo1int(mo_coeff)#

Returns the spin mo 1-electron integrals in physicist’s notation.

Parameters:

mo_coeff (ndarray[Any, dtype[complex128]]) –

Return type:

SpinMO1eInt

class AO2eIntArray(ao2eint_array)#

Bases: AO2eInt

Parameters:

ao2eint_array (npt.NDArray[np.complex128]) –

property array: ndarray[Any, dtype[complex128]]#

Returns the ao 2-electron integrals in physicist’s convention.

to_spatial_mo2int(mo_coeff)#

Returns the spatial mo 2-electron integrals in physicist’s convention.

Parameters:

mo_coeff (ndarray[Any, dtype[complex128]]) –

Return type:

SpatialMO2eIntArray

to_mo2int(mo_coeff)#

Returns the spin mo 2-electron integrals in physicist’s convention.

Parameters:

mo_coeff (ndarray[Any, dtype[complex128]]) –

Return type:

SpinMO2eInt

class AOeIntArraySet(constant: 'float', ao_1e_int: 'AO1eIntArray', ao_2e_int: 'AO2eIntArray')#

Bases: AOeIntSet

Parameters:
constant: float#

constant.

ao_1e_int: AO1eIntArray#

atomic orbital one-electron integral AO1eInt.

ao_2e_int: AO2eIntArray#

atomic orbital two-electron integral AO2eInt.

to_full_space_mo_int(mo)#

Computes the full space spin mo integrals.

Parameters:

mo (MolecularOrbitals) –

Return type:

SpinMOeIntSet

to_full_space_spatial_mo_int(mo)#

Computes the full space spatial mo integrals.

Parameters:

mo (MolecularOrbitals) –

Return type:

SpatialMOeIntSet

to_active_space_mo_int(active_space_mo)#

Computes the active space spin mo integrals.

Note: Does not provide speed advantage compared to PySCFAOeIntSet as it takes additional time to convert ao_eint to mo_eint. Performance penalty grows when the full space mo integral is large.

Parameters:

active_space_mo (ActiveSpaceMolecularOrbitalsBase) –

Return type:

SpinMOeIntSet

to_active_space_spatial_mo_int(active_space_mo)#

Computes the active space spatial mo integrals.

Note: Does not provide speed advantage compared to PySCFAOeIntSet as it takes additional time to convert ao_eint to mo_eint. Performance penalty grows when the full space mo integral is large.

Parameters:

active_space_mo (ActiveSpaceMolecularOrbitalsBase) –

Return type:

SpatialMOeIntSet

class MolecularOrbitals(*args, **kwargs)#

Bases: Protocol

Interface protocol for a data of the molecule.

abstract property n_electron: int#

Returns the number of electrons.

abstract property spin: int#

Returns the total spin of the electrons.

Note

We follow the quantum chemistry convention where:

\[N_{\alpha} - N_{\beta} = 2S\]

and spin = 2S.

abstract property n_spatial_orb: int#

Returns the number of spatial orbitals.

abstract property mo_coeff: ndarray[Any, dtype[complex128]]#

Returns molecular orbital coefficients.

class SpatialMO1eInt(*args, **kwargs)#

Bases: Protocol

Interface protocol for a molecular orbital one-electron integral.

abstract property array: ndarray[Any, dtype[complex128]]#

Returns integral as numpy ndarray.

class SpatialMO1eIntArray(array)#

Bases: SpatialMO1eInt

A class of a molecular orbital one-electron integral.

This interface has an integral as numpy ndarray.

Parameters:

array (npt.NDArray[np.complex128]) –

property array: ndarray[Any, dtype[complex128]]#

Returns integral as numpy ndarray.

class SpatialMO2eInt(*args, **kwargs)#

Bases: Protocol

Interface protocol for a molecular orbital two-electron integral.

abstract property array: ndarray[Any, dtype[complex128]]#

Returns integral as numpy ndarray.

class SpatialMO2eIntArray(array)#

Bases: SpatialMO2eInt

A class of a molecular orbital two-electron integral.

This interface has an integral as numpy ndarray.

Parameters:

array (npt.NDArray[np.complex128]) –

property array: ndarray[Any, dtype[complex128]]#

Returns integral as numpy ndarray.

class SpatialMOeIntSet(const, mo_1e_int, mo_2e_int)#

Bases: NamedTuple

SpatialMOeIntSet holds a constant and a set of molecular orbital electron integral.

Parameters:
const: float#

constant.

mo_1e_int: SpatialMO1eInt#

molecular orbital one-electron integral.

mo_2e_int: SpatialMO2eInt#

molecular orbital two-electron integral.

class SpinMO1eInt(*args, **kwargs)#

Bases: Protocol

Interface protocol for a molecular spin orbital one-electron integral.

abstract property array: ndarray[Any, dtype[complex128]]#

Returns integral as numpy ndarray.

class SpinMO2eInt(*args, **kwargs)#

Bases: Protocol

Interface protocol for a molecular spin orbital two-electron integral.

abstract property array: ndarray[Any, dtype[complex128]]#

Returns integral as numpy ndarray.

class SpinMO1eIntArray(array)#

Bases: SpinMO1eInt

Stores the array of the 1-electron integrals.

Parameters:

array (npt.NDArray[np.complex128]) –

property array: ndarray[Any, dtype[complex128]]#

Returns integral as numpy ndarray.

class SpinMO2eIntArray(array)#

Bases: SpinMO2eInt

Stores the array of the 2-electron integrals.

Parameters:

array (npt.NDArray[np.complex128]) –

property array: ndarray[Any, dtype[complex128]]#

Returns integral as numpy ndarray.

class SpinMOeIntSet(const, mo_1e_int, mo_2e_int)#

Bases: NamedTuple

SpinMOeIntSet holds a constant and a set of molecular orbital electron integral.

Parameters:
const: float#

constant.

mo_1e_int: SpinMO1eInt#

spin molecular orbital one-electron integral.

mo_2e_int: SpinMO2eInt#

spin molecular orbital two-electron integral.

convert_to_spin_orbital_indices(occupied_indices, active_indices)#

Convert each spatial occupied orbital indices and active orbitals indices into the spin occupied orbital indices and active spin indices.

Parameters:

  • occupied_indices (Sequence[int]) – A Sequence of spatial occupied orbital indices.

  • active_indices (Sequence[int]) – A Sequence of spatial active orbital indices.

Return type:

tuple[Sequence[int], Sequence[int]]

get_active_space_spin_integrals_from_ao_eint(active_space_mo, electron_ao_ints)#

Compute the active space spin electron integrals from ao electron integrals.

Parameters:
Return type:

SpinMOeIntSet

get_active_space_spatial_integrals_from_ao_eint(active_space_mo, electron_ao_ints)#

Compute the active space spatial electron integrals from ao electron integrals.

Parameters:
Return type:

SpatialMOeIntSet

get_active_space_spin_integrals_from_mo_eint(active_space_mo, electron_mo_ints)#

Compute the active space spin electron integrals from mo electron integrals.

Parameters:
Return type:

SpinMOeIntSet

get_active_space_spatial_integrals_from_mo_eint(active_space_mo, electron_mo_ints)#

Compute the active space effective core energy and all the spin space electron integrals in the physicist’s convention.

Note: This function yields the active space electron integral faster than pyscf_get_active_space_integrals function in the quri_parts.pyscf package, as it stores the mo electron integrals on memory for computations.

Parameters:
Return type:

SpatialMOeIntSet

get_core_and_active_orbital_indices(n_active_ele, n_active_orb, n_electrons, active_orbs_indices=None)#

Returns sequences of spatial occupied orbital indices and active orbitals indices obtained from the number of active electrons, number of active orbitals, and number of total electrons.

Parameters:

  • n_active_ele (int) – number of active electrons.

  • n_active_orb (int) – number of active orbitals.

  • n_electrons (int) – total number of electrons.

  • active_orbs_indices (Sequence[int] | None) – sequence of spatial orbital indices of the active orbitals.

Return type:

tuple[Sequence[int], Sequence[int]]

get_effective_active_space_core_energy(core_energy, mo_1e_int, mo_2e_int, core_spatial_orb_idx)#

Compute the effective active space core energy for a given active space configuration.

Parameters:

  • core_energy (float) – The full space core erengy.

  • mo_1e_int (ndarray[Any, dtype[complex128]]) – The full space spatial mo 1-electron integral.

  • mo_2e_int (ndarray[Any, dtype[complex128]]) – The full space spatial mo 2-electron integral.

  • core_spatial_orb_idx (Sequence[int]) – The core spatial orbital indices.

Return type:

float

get_effective_active_space_1e_integrals(mo_1e_int, mo_2e_int, core_spatial_orb_idx, active_spatial_orb_idx)#

Compute the effective active space 1-electron spatial integral for a given active space configuration.

Parameters:

  • mo_1e_int (ndarray[Any, dtype[complex128]]) – The orginal space spatial mo 1-electron integral.

  • mo_2e_int (ndarray[Any, dtype[complex128]]) – The orginal space spatial mo 2-electron integral.

  • core_spatial_orb_idx (Sequence[int]) – The core spatial orbital indices.

  • active_spatial_orb_idx (Sequence[int]) –

Return type:

ndarray[Any, dtype[complex128]]

get_effective_active_space_2e_integrals(mo_2e_int, active_spatial_orb_idx)#

Compute the effective active space 2-electron spatial integral for a given active space configuration.

Parameters:

  • mo_1e_int – The orginal space spatial mo 1-electron integral.

  • mo_2e_int (ndarray[Any, dtype[complex128]]) – The orginal space spatial mo 2-electron integral.

  • core_spatial_orb_idx – The core spatial orbital indices.

  • active_spatial_orb_idx (Sequence[int]) –

Return type:

ndarray[Any, dtype[complex128]]

spatial_mo_eint_set_to_spin_mo_eint_set(spatial_mo_eint_set)#

Compute the spin space mo_eint_set from spatial mo_eint_set.

Parameters:

spatial_mo_eint_set (SpatialMOeIntSet) –

Return type:

SpinMOeIntSet

to_spin_orbital_integrals(n_spin_orb, spatial_1e_integrals, spatial_2e_integrals)#

Convert spatial orbital electron integrals to spin orbital electron integrals.

Parameters:

  • n_spin_orb (int) –

  • spatial_1e_integrals (ndarray[Any, dtype[complex128]]) –

  • spatial_2e_integrals (ndarray[Any, dtype[complex128]]) –

Return type:

tuple[ndarray[Any, dtype[complex128]], ndarray[Any, dtype[complex128]]]

spatial_mo_1e_int_to_spin_mo_1e_int(n_spin_orb, spatial_1e_integrals)#

Convert spatial mo 1e electron integrals to spin mo 1e electron integrals.

Parameters:

  • n_spin_orb (int) –

  • spatial_1e_integrals (ndarray[Any, dtype[complex128]]) –

Return type:

ndarray[Any, dtype[complex128]]

spatial_mo_2e_int_to_spin_mo_2e_int(n_spin_orb, spatial_2e_integrals)#

Convert spatial mo 2e electron integrals to spin mo 2e electron integrals.

Parameters:

  • n_spin_orb (int) –

  • spatial_2e_integrals (ndarray[Any, dtype[complex128]]) –

Return type:

ndarray[Any, dtype[complex128]]

Submodules#